Recursive Bayesian Method for Estimating States of Nonlinear System from Sequential Indirect Observations

Recursive Bayesian equations are given for estimating the states of a system, given the sequence of inputs, outputs, and the probabilistic interdependences from one time to the next. Equations are derived for the case of a nonlinear system with normal error densities and linear deviations for small errors. These equations reduce to the Kalman filter for the strictly linear case. When the equations are applied to a specific nonlinear system, i.e., a transversal sampled data filter with unknown weighting states, a perceptron or Adaline type algorithm results for estimating the weights.